The physics
A ball let go in a liquid feels three forces. The weight pulls it down. The buoyancy and the drag push it up.
buoyancy = σ V g drag = 6πηrv (Stokes' law)
The drag grows with the speed. So the ball speeds up only for a short time. Soon the drag and the buoyancy match the weight. After that it falls at a steady speed, its terminal speed.
vt = 2r²(ρ − σ)g / 9η
Here ρ is the ball's density and σ is the liquid's. Take the viscosity η in Pa·s. One poise is 0.1 Pa·s.
A bubble has almost no weight. Its buoyancy alone matches the drag, so it rises at 2r²σg / 9η.
The terminal speed goes as r². A ball twice as wide falls 4 times as fast. When n equal drops merge, the radius grows n1/3 times.
vt ∝ r² R = n1/3 r
A ball that enters the liquid at its terminal speed keeps that speed. A free fall from a height h gives v² = 2gh.